Battery Issues

Hi, we are having this issue with our 2004 Concorde 2.7 liter where the car starts and runs fine for days, then out of no where the battery is dead. I assumed the first time that a light must have been left on or something because it took a boost fine, ran fine, then restarted after being driven for 10 minutes on its own.

Then it worked for a couple of days no problems, but then this morning, dead battery. I am reluctant to change the battery or alternator because it seems weird that they work, it seems more likely to me that something is putting a drain on the battery.

I have read that a voltage regulator can cause these types of isses, does that make sense? Any other ideas?